Three-Dimensional Analysis of the Free Vibrations of Layered Composite Plates Based on the Semianalytic Finite-Element Method

2020 ◽  
Vol 56 (4) ◽  
pp. 481-497
Author(s):  
A. V. Marchuk ◽  
S. V. Reneiskaya ◽  
O. N. Leshchuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Composite Plates ◽  
Free Vibrations ◽  
Layered Composite ◽  
Element Method

GENERALIZED FINITE ELEMENT METHOD FOR NONLINEAR THREE-DIMENSIONAL ANALYSIS OF SOLIDS

2008 ◽  
Vol 05 (01) ◽  
pp. 37-62 ◽  
Author(s):  
SERGIO PERSIVAL BARONCINI PROENÇA ◽  
IVAN FRANCISCO RUIZ TORRES
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dimensional Analysis ◽  
Damage Model ◽  
Three Dimensional ◽  
Generalized Finite Element Method ◽  
Good Tool ◽  
Selective Enrichment ◽  
Generalized Finite Element ◽  
Element Method

The Generalized Finite Element Method (GFEM) is employed in this paper for the numerical analysis of three-dimensional solids under nonlinear behavior. A brief summary of the GFEM as well as a description of the formulation of the hexahedral element based on the proposed enrichment strategy are initially presented. Next, in order to introduce the nonlinear analysis of solids, two constitutive models are briefly reviewed: Lemaitre's model, in which damage and plasticity are coupled, and Mazars's damage model suitable for concrete under increased loading. Both models are employed in the framework of a nonlocal approach to ensure solution objectivity. In the numerical analyses carried out, a selective enrichment of approximation at regions of concern in the domain (mainly those with high strain and damage gradients) is exploited. Such a possibility makes the three-dimensional analysis less expensive and practicable since re-meshing resources, characteristic of h-adaptivity, can be minimized. Moreover, a combination of three-dimensional analysis and the selective enrichment presents a valuable good tool for a better description of both damage and plastic strain scatterings.

Global Local Finite Element Method (GLFEM) in Gear Tooth Stress Analysis

1993 ◽  
Vol 115 (4) ◽  
pp. 1008-1012 ◽  
Author(s):  
I. Moriwaki ◽  
T. Fukuda ◽  
Y. Watabe ◽  
K. Saito
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Analysis ◽  
Dimensional Analysis ◽  
Gear Tooth ◽  
Three Dimensional ◽  
Critical Section ◽  
Energy Principle ◽  
Analysis Technique ◽  
Element Method

The present study is concerned with an application of the global local finite element method (GLFEM) to a gear tooth stress analysis. The GLFEM is a numerical analysis technique which combines finite element solutions and classical analytical ones on the basis of the energy principle. In this method, the classical analytical solutions give an almost exact stress field to the elements in which the stress varies very rapidly and/or the stress concentration is found. A fine subdivision, therefore, is not required. In the application of the conventional finite element method to the gear tooth stress analysis, the fine subdivision is required especially at the positions near tooth bottom and the load applied point. Hence, only two-dimensional analysis is available for common use. Furthermore, in order to determine an exact location of a critical section on which a fillet stress is maximum, we must use complicated procedures, e.g., an iteration of subdivision for searching the maximum nodal stress. In the present paper, the GLFEM is applied to the gear tooth stress analysis to show that even the rough subdivision enables us to make the precise three-dimensional analysis. It also guarantees an easy determination of the critical section. Thus, we show the effective future of the GLFEM to the gear tooth stress analysis.

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